The law of reciprocity in acoustics and elastodynamics codifies a relation of symmetry between action and reaction in fluids and solids. In its simplest form, it states that the frequency response functions between any two material points remain the same after swapping source and receiver, regardless of the presence of inhomogeneities and losses. As such, reciprocity has enabled numerous applications that make use of acoustic and elastic wave propagation. A recent change in paradigm has prompted us to see reciprocity under a new light: as an obstruction to the realization of wave-bearing media in which the source and receiver are not interchangeable. Such materials may enable the creation of devices such as acoustic one-way mirrors, diodes and topological insulators. Here, we review how reciprocity breaks down in materials with momentum bias, structured space-dependent and timedependent constitutive properties, and constitutive nonlinearity, and report on recent advances in the modeling and fabrication of these materials, as well as on experiments demonstrating nonreciprocal acoustic and elastic wave propagation therein. The success of these efforts holds promise to enable robust, unidirectional acoustic and elastic wave steering capabilities that exceed what is currently possible in conventional materials, metamaterials or phononic crystals.

Acoustic waves in a linear time-invariant medium are generally reciprocal, however, reciprocity can break down in a time-variant system. In this paper, we report on an experimental demonstration of non-reciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional bandgap in the dispersion relation. A theoretical explanation of the observed non-reciprocal behavior is provided as well. This work provides a prototype for developing acoustic diode that can serve in acoustic circuits for rectification applications .

Stubbed plates, i.e., thin elastic sheets endowed with pillar-like scatterers, display subwavelength, locallyresonant bandgaps that are controlled by both the intrinsic resonance properties of the pillars and by the relative stiffness of the pillars to the baseplate. In this work, we focus on the response of a thin and compliant plate featuring heterogeneous families of pillars. We demonstrate experimentally that both the spatial arrangement and the resonant frequencies of the pillars greatly influence the filtering characteristics of the system. We highlight that both spatially graded as well as random (disordered) arrangements of pillars result in macroscopic bandgap widening. We further report that the spectral range over which wave attenuation achieved with random arrangements is on average wider than the one observed while working with graded configurations. We explore the robustness of these findings against small changes in the structural and material properties of the plate and pillars.

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